SDP bounds on quantum codes: rational certificates
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Quantum Physics arXiv:2603.19901 (quant-ph) [Submitted on 20 Mar 2026] Title:SDP bounds on quantum codes: rational certificates Authors:Gerard Anglès Munné, Felix Huber View a PDF of the paper titled SDP bounds on quantum codes: rational certificates, by Gerard Angl\`es Munn\'e and Felix Huber View PDF HTML (experimental) Abstract:A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum linear programming bounds. However, floating-point inaccuracies prevent the extraction of rigorous non-existence proofs from the numerical methods. Here, we address this by providing rational infeasibility certificates for a range of quantum codes. Using a clustered low-rank solver with heuristic rounding to algebraic expressions, we can improve upon $18$ upper bounds on the maximum size of $n$-qubit codes with $6 \leq n \leq 19$. Our work highlights the practicality and scalability of semidefinite programming for quantum coding bounds. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2603.19901 [quant-ph] (or arXiv:2603.19901v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.19901 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Gerard Anglès Munné [view email] [v1] Fri, 20 Mar 2026 12:33:38 UTC (125 KB) Full-text links: Access Paper: View a PDF of the paper titled SDP bounds on quantum codes: rational certificates, by Gerard Angl\`es Munn\'e and Felix HuberView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cs cs.IT math math.IT References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)